Information and Economics:
A Critique of Hayek

Allin F. Cottrell and W. Paul Cockshott

October, 1994

Abstract

The report presents Hayek,s arguments about the use of
information in economics and asseses their adequacy.
They are criticised both with respect to their subjectivist
philosophical foundations, and by applying the
techniques of information theory. We use information theory
to show that Hayek underestimates the information costs involved
in the operation of the market and overestimates the
information costs of detail planning.

Neither the theoretical arguments put forward in the West, nor the fact of
the collapse of Soviet socialism, historic landmark as it undoubtedly is,
warrant the belief that socialist economic planning tout court is an
untenable notion whose time has passed. Indeed, modern developments in
information technology open up the possibility of a
planning system that could outperform the market in terms of efficiency (in
meeting human needs) as well as equity. Such are the claims that we have
defended in a number of recent publications, designed to re-open a debate
over socialist economics.1
We
do not expect that our ideas will meet with immediate political
success, but we do venture to hope that open-minded economists will
consider our economic arguments on their merits.

We do not intend to reiterate our general arguments in favour of planning
here.
Our object is to refute the objections to socialist planning put forward by
Hayek in his classic article `The Use of Knowledge in Society' (1945).
The relevance of such an argument to the readership of this journal might
be questioned. Doesn't Hayek lie outside of the mainstream of British
(increasingly, Anglo-American) professional economics, with its dual roots
in Marshallian pragmatism and the formal general equilibrium theory of the
Lausanne school? Wasn't Hayek's defence of the market always a bit too
strident and doctrinaire to suit the sensibilities of a profession that (in
Britain at any rate) has traditionally had a broadly social-democratic
outlook? Maybe so, but it is our impression that Hayek's star is on the rise
in the post-Communist world, and that even those who baulk at his
extreme enthusiasm for the unfettered market are often quite
ready to see his
arguments used to bury any form of thorough-going socialism.

And so to business. We offer below an exposition and point-by-point
contestation of the ideas in Hayek (1945). We should make it clear that
some, though by no means all, of our criticisms of Hayek are
anachronistic-that is, they depend on advances in information technology
that have taken place since Hayek wrote. We think this is justified for
two reasons. First, Hayek clearly thought he was putting forward a very
general argument, which he did not expect to see undermined by
technological change. Second, Hayek's followers (e.g. Lavoie,
1985) continue to support his arguments of several decades ago, and to
assert that developments in information technology are largely beside the
point.

In our exposition of Hayek we try to balance concision with the need
to produce a sufficiently full and fair account to obviate the suspicion
that we may be attacking a straw man. We begin with a brief summary of the
philosophical views that inform the argument of `The Use of Knowledge in
Society', which are spelled out more fully in The Counter-Revolution
of Science (Hayek, 1955).

In The Counter Revolution of Science Hayek is concerned to
contrast the natural and social sciences, whose relation to their subject
matter, he claims, is fundamentally different. In the natural sciences,
advances involve recognising that things are not what they seem.
Science dissolves the immediate categories of subjective experience and
replaces them with underlying, often hidden, causes. The study of
society on the other hand has to take as its raw material the ideas and
beliefs of people in society. The facts studied by social science

differ from the facts of the physical sciences in being beliefs or opinions
held by particular people, beliefs which as such are our data, irrespective
of whether they are true or false, and which, moreover, we cannot
directly observe in the minds of people but which we can recognise from
what they say or do merely because we have ourselves a mind similar to
theirs. (Hayek, 1955, p. 28)

He argues that there is an irreducible subjective element to the subject
mater of the social sciences which was absent in the physical sciences.

[M]ost of the objects of social or human action are not ``objective facts" in
the special narrow sense in which the term is used in the Sciences and
contrasted to ``opinions", and they cannot at all be defined in physical
terms. So far as human actions are concerned, things are what
the acting people think they are. (Hayek, 1955, pp. 27-27)

His paradigm for the social or moral sciences is that society must be
understood in terms of men's conscious reflected actions, it being
assumed that people are constantly consciously choosing between
different possible courses of action. Any collective phenomena must thus
be conceived of as the unintended outcome of the decisions of individual
conscious actors.

This imposes a fundamental dichotomy between the study of nature and
of society, since in dealing with natural phenomena it may be reasonable
to suppose that the individual scientist can know all the relevant
information, while in the social context this condition cannot possibly be
met.

From this philosophical ground Hayek (1945) poses the question: `What is the
problem we wish to solve when we try to construct a rational economic
order?'

He continues:

On certain familiar assumptions the answer is simple enough. If we
possess all the relevant information, if we can start out from a given
system of preferences and if we command complete knowledge of
available means, the problem which remains is purely one of logic. That
is, the answer to the question of what is the best use of the available
means is implicit in our assumptions. The conditions which the solution of
this optimum problem must satisfy have been fully worked out and can
be stated best in mathematical form: put at their briefest, they are that
the marginal rates of substitution between any two commodities or
factors must be the same in all their different uses. (Hayek, 1945, p.
519)

He immediately makes it clear, however, that the `familiar assumptions'
upon which the above approach is predicated are quite unreal.

This, however, is emphatically not the economic problem which society
faces ¼ The reason for this is that the data from which the
economic calculus starts are never for the whole society given to a
single mind which could work out the implications, and can never be so
given. (ibid .)

Hayek then spells out his own perspective on the nature of the problem:

The peculiar character of the problem of a rational economic order is
determined precisely by the fact that the knowledge of the
circumstances of which we must make use never exists in concentrated
or integrated form, but solely as the dispersed bits of incomplete and
frequently contradictory knowledge which all the separate individuals
possess. (ibid .)

The true problem is therefore ``how to secure the best use of resources
known to any of the members of society, for ends whose relative
importance only these individuals know'' (Hayek, 1945, p. 520,
emphasis added). That this is not generally understood, Hayek claims, is
an effect of naturalism or scientism, that is ``the erroneous transfer to
social phenomena of the habits of thought we have developed in dealing
with the phenomena of nature'' (ibid .).

The point at issue between Hayek and the proponents of socialist
economic planning is not ``whether planning is to be done or not''.
Rather it is ``whether planning is to be done centrally, by one authority
for the whole economic system, or is to be divided among many
individuals'' (Hayek, 1945, pp. 520-21). The latter case is nothing other
than market competition, which ``means decentralized planning by many
separate persons'' (Hayek, 1945, p. 521). And the relative efficiency of
the two alternatives hinges on

whether we are more likely to succeed in putting at the disposal of a
single central authority all the knowledge which ought to be used but
which is initially dispersed ¼ or in conveying to individuals such
additional knowledge as they need in order to fit their plans in with those
of others. (ibid .)

The next step in Hayek's argument involves distinguishing two different
kinds of knowledge: scientific knowledge (understood as knowledge of
general laws) versus ``unorganized knowledge'' or ``knowledge of the
particular circumstances of time and place''. The former, he says, may
be susceptible of centralization via a ``body of suitably chosen experts''
(Hayek, 1945, p. 521) but the latter is a different matter.

[P]ractically every individual has some advantage over others in that he
possesses unique information of which beneficial use might be made,
but of which use can be made only if the decisions depending on it are
left to him or are made with his active cooperation. (Hayek, 1945, pp.
521-22)

Hayek is thinking here of ``knowledge of people, of local conditions, and
special circumstances'' (Hayek, 1945, p. 522), e.g., of the fact that a
certain machine is not fully employed, or of a skill that could be better
utilized. He also cites the sort of specific, localised knowledge relied
upon by shippers and arbitrageurs. He claims that this sort of
knowledge is often seriously undervalued by those who consider general
scientific knowledge as paradigmatic.

Closely related, in Hayek's mind, to the undervaluation of knowledge of
local and specific factors is underestimation of the role of change in
the economy. One key difference between advocates and critics of
planning concerns

the significance and frequency of changes which will make substantial
alterations of production plans necessary. Of course, if detailed
economic plans could be laid down for fairly long periods in advance and
then closely adhered to, so that no further economic decisions of
importance would be required, the task of drawing up a comprehensive
plan governing all economic activity would appear much less formidable.
(Hayek, 1945, p. 523)

Hayek ascribes to his opponents the idea that economically-relevant
change is something that occurs at discrete intervals and on a fairly long
time-scale, and that in between such changes the management of the
productive system is a more or less mechanical task. As against this, he
cites, for instance, the problem of keeping cost from rising in a
competitive industry, which requires considerable day-to-day managerial
energy, and he emphasises the fact that the same technical facilities may be
operated at widely differing cost levels by different managements.
Effective economical management requires that ``new dispositions [be]
made every day in the light of circumstances not known the day before''
(Hayek, 1945, p. 524). He therefore concludes that

central planning based on [aggregated] statistical information by its
nature cannot take direct account of these circumstances of time and
place, and ¼ the central planner will have to find some way or
other in which the decisions depending upon them can be left to the man
on the spot. (ibid .)

Rapid adaptation to changing circumstances of time and place requires
decentralisation-we can't wait for some central board to issue orders
after integrating all knowledge.

While insisting that very specific, localised knowledge is essential to
economic decision making, Hayek clearly recognises that the ``man on
the spot'' needs to know more than just his immediate circumstances
before he can act effectively. Hence there arises the problem of
``communicating to him such further information as he needs to fit his
decisions into the whole pattern of changes of the larger economic
system'' (Hayek, 1945, p. 525) How much does he need to know?
Fortuitously, only that which is conveyed by prices. Hayek constructs an
example to illustrate his point:

Assume that somewhere in the world a new opportunity for the use of
some raw material, say tin, has arisen, or that one of the sources of
supply of tin has been eliminated. It does not matter for our purpose and
it is very significant that it does not matter which of these two causes
has made tin more scarce. All that the users of tin need to know is that
some of the tin they used to consume is now more profitably employed
elsewhere, and that in consequence they must economize tin. There is no
need for the great majority of them even to know where the more urgent
need has arisen, or in favor of what other uses they ought to husband the
supply. (Hayek, 1945, p. 526)

Despite the absence of any such overview, the effects of the
disturbance in the tin market will ramify throughout the economy just the
same.

The whole acts as one market, not because any of its members survey
the whole field, but because their limited individual fields of vision
sufficiently overlap so that through many intermediaries the relevant
information is communicated to all. (ibid .)

Therefore the significant thing about the price system is ``the economy
of knowledge with which it operates'' (Hayek, 1945, pp. 526-7). He
drives his point home thus:

It is more than a metaphor to describe the price system as a kind of
machinery for registering change, or a system of telecommunications
which enables individual producers to watch merely the movement of a
few pointers, as an engineer might watch the hands of a few dials, in
order to adjust their activities to changes of which they may never know
more than is reflected in the price movements. (Hayek, 1945, p. 527)

He admits that the adjustments produced via the price system are not
perfect in the sense of general equilibrium theory, but they are
nonetheless a ``marvel'' of economical coordination. (ibid .)

The price system has not, of course, arisen as the product of human
design, and moreover ``the people guided by it usually do not know why
they are made to do what they do'' (ibid .). This observation leads
Hayek to a very characteristic statement of his general case against
central planning.

[T]hose who clamour for ``conscious direction''-and who cannot
believe that anything which has evolved without design (and even
without our understanding it) should solve problems which we should not
be able to solve consciously-should remember this: The problem is
precisely how to extend the span of our utilization of resources beyond
the span of the control of any one mind; and, therefore, how to provide
inducements which will make individuals do the desirable things without
anyone having to tell them what to do. (Hayek, 1945, p. 527)

Hayek generalises this point by reference to other ``truly social
phenomena'' such as language (also an undesigned system). Against the
idea that consciously designed systems have some sort of inherent
superiority over those that have merely evolved, he cites A. N.
Whitehead to the effect that the progress of civilisation is measured by
the extension of ``the number of important operations which we can
perform without thinking about them'' (Hayek, 1945, p. 528). He
continues:

The price system is just one of those formations which man has learned
to use¼ after he had stumbled upon it without understanding it.
Through it not only a division of labor but also a coordinated utilization of
resources based on an equally divided knowledge has become
possible¼ [N]obody has yet succeeded in designing an alternative
system in which certain features of the existing one can be preserved
which are dear even to those who most violently assail it such as
particularly the extent to which the individual can choose his pursuits and
consequently freely use his own knowledge and skill. (ibid .)

The outline of Hayek's argument is now, we trust, clearly in view.
We are ready to proceed to our criticisms, which are structured as follows.
We first challenge the subjectivist philosophy that underpins
Hayek's conception of information. We then offer an alternative
perspective on the nature of the problem faced by a planned economic
system, and we dispute Hayek's claims regarding the benefits of
decentralisation. This then leads into a critique of the idea that
the market constitutes an efficient telecommunications system. Our
critique is developed by means of a formal model of the information
exchanges required under market and plan. The penultimate section of
the paper deals with the idea that change is all important; and the
concluding section takes up the issue of the market as a `spontaneously
evolved' system.

Hayek's radically subjectivist view of the social
sciences is open to the objection that its constitutive category, the
rational subject, is by no means obviously given. As Lawson (1992) has
argued, a wealth of psychological and sociological
research has revealed that human behaviour is highly routinized, and
coordinated in the main by unconscious brain functions. Indeed, as
Dennett (1991) relates, experiments in neuropsychology
indicate that people act first and become concious of their
intention to act later.

For the more limited domain of economics, there is the problem that
the `subjects' in question are more likely to be juridical than personal.
In the main, the economic actors in industrial production are firms, not
human individuals. Nor can the actions of a firm be reduced to the
inner subjective life of its managing director. In any large firm, the
courses of action taken result from a complex set of practices,
reviews, and decision-making procedures involving many people, and
in which the procedures can be as important as who fills which particular
positions. We would argue that the economic subject that Hayek
takes as his starting point is not empirically given at all,
but is rather a reification of economic theory. The rational economic
subject makes sense only in terms of formalised calculating
procedures, which, if they are realised in practice, are more
likely to be materialised in the accounting and management practices
of firms than in the brains of individuals. Economic theory then
projects back these practices, rational for the enterprise as a juridical
subject, onto a supposedly constitutive human subject.

The historical conditions for this projection are clear enough. In
the early stages of capitalism the distinction between personal and
juridical subjects was as yet ill defined. The agent of economic
practice thus appeared to be the person of the capitalist or
entrepreneur rather than the firm. But from the standpoint of the
current state of economic development, it can be seen that the
rational calculating subject is the property-maximising juridical
subject. To the extent that in a property system some of the juridical
subjects are individual human animals, the reified subject of economic
theory provides an account of what would be rational action on their
part. But the assertion that these animals do engage
in such rational action is more an act of faith than an empirical
result of science. By starting out with this act of faith Hayek aimed to
mark off economics as essentially a branch of moral philosophy rather
than science.

But once the category of subject is recognised for what it is, not an
empirically existing property of the human animal, but something
ascribed to it both by the structures of language and of juridical
discourse (Althusser, 1971), then this exclusion of science from the
study of society becomes untenable. It becomes just one more of the
special pleas by morality to hold the encroachments of science at
bay.

Hayek's subjectivist philosophical standpoint has an important bearing on
his arguments against socialist planning, since these
arguments hinge on the notion of subjective information.
Despite the fact that The Counter-Revolution
of Science was published after the establishment of a scientific
information theory by Shannon and Weaver (1949), Hayek's notion of
information remains resolutely pre-scientific. Admittedly, it takes
time for the discoveries of one discipline to percolate through
to others. In the mid-1950s the idea of the objectivity of information
had not yet spread far
beyond the study of telecommunications. But now, when it has
revolutionised biology, become the foundation of our major industries,
and begun to transform our understanding of social ideologies
(Dawkins, 1982), its absence vitiates Hayek's entire argument.

For Hayek information is essentially subjective; it is knowledge in
people's minds. Thus we have the problem of how
information that is dispersed in the minds of many can, through the
operations of the market, be combined for the common good. By
taking this subjectivist standpoint, attention is diverted away from the
very practical and important question of the technical supports for
information. It becomes impossible to see the production and
manipulation of information as both a technology and a labour process
in its own right, whose development acts as a constraint upon the
possibility of economic relations.

In any but the most primitive of economies, economic relations have
depended upon the development of techniques for objectifying
information. Consider the relationship between landlord and tenant,
and thus rent. This can only stabilise once society has a means for
recording ownership and tenancy contracts, whether as written
documents or the mortgage marker stones so hated by the peasantry
of Attica.

The development of price relies upon the technology of counting and
calculation, which can never in a commercial society be a purely
mental operation. Calculation demands a material support, whether
it be the calculi or small stones of the early Romans, or the coins and
reckoning tables of late Antiquity and the middle ages. Economic
rationality is an algorithmic process supported by a machinery for
computation and information storage. The fact that until recently the
machinery was simple and hand-operated-the abacus, the coin box,
or the ledger-allowed it to be ignored in economic theory. But the
means of rationality are as essential to economic relations as the
means of production. Trade without a technology of calculation and
record is as impractical as agriculture without instruments to turn the
soil. Once these aspects of information theory and information
technology are considered, quite different answers can be given to
Hayek's problem of economic information.

We have argued elsewhere (Cottrell and Cockshott, 1993a)
that the classic `socialist calculation
debate' in the first part of this century took place on the terrain of the
neoclassical critics of socialism rather than its Marxian advocates.
This had an effect in defining the structure of the problem. In the
neoclassical variant, the problem starts with the preferences of the
individual agents and their production possibilities. This formulation is
vulnerable to Hayek's critique, on the grounds that individuals' preferences
are in no sense `given' to the planners. But Marxian economists would
not accept that these individual preferences have any meaningful pre-existence;2
they do not, therefore, form part of the problem.

The practical problem is to bring production potential into alignment
with a pattern of social need revealed by a combination of
democratic political decisions (as in the case of, say, the appropriate
level of public health service provision) and aggregate consumer
purchases. Given a reasonable data-collection system reporting on the
rates at which consumer goods are selling, and assuming a pricing
system based on labour values (Cockshott and Cottrell, 1993),
deriving a target net-output vector
demands no special telepathic powers on the part of the planning
system. It is perhaps harder to gather the information about
production possibilities. It is in this practical context that Hayek's
discussion of centralised versus decentralised control systems must
be placed.

Austrian opponents of socialism talk as if socialist planning has to be
carried out by one man. Mises (1949) personified him as `the director'.
Hayek continues the metaphor, stating that the ``data from which the
economic calculus starts are never for the whole society given to a
single mind". How then, he asks, can one mind presume to improve on the
combined result of the cogitations of millions (as achieved via
the market)? Surely only a megalomaniac, or at any rate one blinded
by scientific hubris, could propose such a thing.

Of course no single individual has the brainpower to understand all of
the interconnections of an economy, but when have socialists ever
asserted anything so foolish? Not even the most avid personality
cultists claimed that Stalin drew up the 5-year plans himself. What
socialists have proposed is the replacement of market information
processing by the processing of economic information within a
planning organisation. In the past, because of technological limitations,
the planning organisation has proceeded by a division of mental labour
among a large number of people. In the future, the information
processing is likely to be done mainly by computing machines.

In neither case-and here our critique of Hayek's subjectivism comes
into play-is the information concentrated in one mind. In the
former case it is obviously not in the mind of a single worker, but it is
not even in the minds of a collection of workers. Instead, the
information is mainly in their written records, forms, ledgers, etc.
These constitute the indispensible means of administration. From
the earliest temple civilisations of Sumer and the Nile,
the development of economic administration was predicated upon
the development of means of calculation and record. The human
mind enters in as an initial recorder of information, and then as a
manipulator of the recorded information. By procedures of calculation
strings of symbols are read and transformed ones written down. The
symbols-whether they be arabic numerals, notches on tally sticks or
quipu-represent physical quantities of goods; their transformations
model actual or potential movements of these goods.

By posing the question in terms of concentrating the information in a
single mind, Hayek harks back to a pre-civilised condition, abstracting
from the real processes that make any form of administration
possible. If instead, his objection is that no system of administration
can possibly have the information-processing capacity required for
the task, then he is liable to the attack that information technology has
revolutionised the amount of information that can be effectively
administered.

The dichotomy that Hayek operates between the natural sciences and
the social domain also leaves its imprint on his categorisation of
forms of knowledge. In his view, there are but two such forms: knowledge
of general scientific laws, and (subjective) knowledge of `particular
circumstances of time and place'. But this leaves out of account a
whole layer of knowledge that is crucial for economics, namely knowledge
of specific technologies. Such knowledge is not reducible to general scientific
law (it is generally a non-trivial problem to move from a relevant
scientific theory to a workable industrial innovation), but neither
is it so time- or place-specific that it is non-communicable. The
licensing and transfer of technologies in a capitalist context shows
this quite clearly. A central registry of available technologies would
form as essential component of an efficient planning system.
How would such information be assembled? Again, Hayek's notion of
knowledge existing solely `in the mind' is an obstacle to understanding.
It is increasingly common-indeed, it is by now all but universal practice-for firms to keep records of their inputs and outputs in the form of
some sort of computer spreadsheet. These computer files form an
image of the firm's input-output characteristics, an image which is
readily transferable.3

Further, even the sort of `particular' knowledge which Hayek thought too
localised to be susceptible to centralisation is now routinely
centralised. Take his example of the information possessed by shippers.
In the 1970s American Airlines achieved the position of the world's
largest airline, to a great extent on the strength of their
development of the SABRE system of computerised booking of flights
(Gibbs, 1994). Since then we have come to take it for granted that
our local travel agent will be able to tap into a computer network
to determine where and when there are flights available from just about
any A to any B across the world. Hayek's appeal to localised knowledge
in this sort of context may have been appropriate at the time of writing,
but it is now clearly outdated.

We would not dispute, however, that some localised knowledge,
important for the fine-grained efficiency of the system, may be too
specific for any meaningful centralisation. Our objection here is that
Hayek seems to overlook the possibility that this sort of
knowledge may simply be used locally, without prejudice to the operation of
a central plan. The question here concerns the degree of
recursiveness of planning, that is, the extent to which plans can be
formulated in general terms by the higher planning authorities, to be
specified in progressively fuller detail by successively lower or more
local instances. Nove (1977, 1983) has argued persuasively that
as regards the composition of output, the degree of recursiveness of
planning is rather small. If a central authority sets output targets in
aggregated terms, and leaves it to lower instances to specify the
details, the result is bound to be incoherent. In the absence of the sort
of horizontal links between enterprises characteristic of the market
system, the enterprises simply cannot know what specific sort of
output will be needed, unless they are told this by the planning authority.
This may be granted.4
But low recursiveness with respect to
decisions on the composition of output does not imply that all
decisions relating to production have to be taken centrally. Consider
the knowledge, at the level of the enterprise, of which particular
workers are best at which tasks, who is the fastest worker and who
the most reliable and so on (and similarly for the particular machines
operated within the enterprise). Why shouldn't such knowledge just
be used locally in drawing up the enterprise's own detailed schedules
for meeting an output plan given from the `centre'? Isn't this precisely
what happens at plant level in the context of planning by a large
(multiplant) capitalist enterprise?

Having argued that the centralisation of much economic information
is feasible, we now consider its desirability.
When economic calculation is viewed as a computational process,
the advantages of calculation on a distributed or decentralised
basis are far from evident; the question hinges on
how a multiplicity of facts about production possibilities in different
branches of the economy interrelate. Their interrelation is, partially,
an image in the field of information of the real interrelation of the
branches of the economy. The outputs of one activity act as inputs
for another: this is the real interdependence. In addition, there
are potential interactions where different branches of
production function as alternative users of inputs.

It is important to distinguish the two types of interaction. The first
represents real flows of material and is a static property of a
snapshot of the economy. The second, the variation in potential uses
for goods, is not a property of the real economy but of the phase
space of possible economies.
The latter is part of the economic problem insofar as this is considered
to be a search for optimal points within this phase space. In a market
economy, the evolution of the real economy-the real
interdependencies between branches-provides the search procedure
by which these optima are sought. The economy describes a
trajectory through its phase space. This trajectory is the product of
the trajectories of all of the individual economic agents, with these
individual agents deciding upon their next position on the basis of the
information they get from the price system.

Following up on Hayek's metaphor of the price system as telecoms system
or machinery for registering changes, the market economy as a
whole acts as a single analog processor. A single processor,
because at any one point in time it can be characterised by a single
state vector that defines its position in the phase space of the
economic problem. Moreover, this processor operates with a very
slow cycle time, since the transmission of information is bounded by
the rate of change of prices. To produce an alteration in prices, there
must be a change in the real movement of goods (we are abstracting
here from the small number of highly specialised futures markets).
Thus the speed of information transmission is tied to the speed with
which real goods can be moved or new production facilities brought
on line. In sum, a market economy performs a
single-threaded seach through its
state space, with a relatively slow set of adjustments to its position,
the speed of adjustments being determined by how fast the real
economy can move.

Contrast this now with what can potentially be
done if the relevant facts can be concentrated, not in one place-that
would be impossible-but within a small volume of space.
If the information is gathered into one or
more computing machines, these can search the possible state space
without any change in the real economy.

Here the question of whether to concentrate the information is very
relevant. It is a basic property of the universe that no portion of it can
affect another in less time than it takes for light to propagate between
them. Suppose one had all the relevant information spread around a
network of computers across the country. Assume any one of these
could send a message to any other. Suppose that this network was
now instructed to simulate possible states of the economy in
order to search for optima. The evolution from one simulated state to
another could proceed as fast as the computers could exchange
information regarding their own current state. Given that
electronic signals between them travel at the speed of light this will
be far faster than a real economy can evolve.

But the speed of evolution will be much faster still if we bring
all of the computers into close proximity to
one another. Massively parallel computers attempt to place all the
processors within a small volume, thereby allowing signals
moving at the speed of light to propagate around the machine in a
few nanoseconds, compared to the hundredths of a second required
for telecoms networks. Hence, in general, if one wishes to solve a
problem fast, the information required should be placed in the smallest
possible volume.

It may be objected that the sheer scale of the economic problem is
such that although conceivable in principle, such computations would be
unrealisable in practice (Hayek, 1955;5
see also Nove, 1983). We have established
elsewhere (Cockshott and Cottrell, 1993; Cottrell and Cockshott, 1993b)
that given modern computer technology this is far from the case.

Prices, according to Hayek, provide the telecoms system of the
economy. But how adequate is this telecoms system and how much
information can it really transmit?

Hayek's example of the tin market bears careful examination. Two preliminary
points should be made. First, the market system does manage to
achieve a reasonable degree of coordination of economic activities.
The ``anarchy of the market'' (Marx) is far from total chaos. Second,
even in a planned system there will always be scope for the
disappointment of expectations, for projects that looked promising ex
ante to turn out to be failures and so on. Failures of coordination are
not confined to market systems. That said, it is nonetheless clear
that Hayek grossly overstates his case. In order to make rational
decisions relating to changing one's usage of tin, one has to know
whether a rise in price is likely to be permanent or transient, and that
requires knowing why the price has risen. The current price signal is
never enough in itself. Has tin become more expensive temporarily,
due, say, to a strike by the tin miners? Or are we approaching the
exhaustion of readily available reserves? Actions that are rational in
the one case will be quite inappropriate in the other.

Prices in themselves provide adequate knowledge for rational
calculation only if they are at their long-run equilibrium levels, but of
course for Hayek they never are. On this point it is useful to refer
back to Hayek's own theory of the trade cycle (Hayek, 1935; see
also Lawlor and Horn, 1992; Cottrell, 1994), in which the
`misinformation' conveyed by disequilibrium prices can cause very
substantial macroeconomic distortions. In Hayek's cycle theory, the
disequilibrium price that can do such damage is the rate of interest,
but clearly the same sort of argument applies at the micro level too.
Decentralised profit-maximising responses to unsustainable prices for
tin or RAM chips are equally capable of generating
misinvestment and subsequent chaos.

At minimum, prices may be said to carry information regarding the
terms on which various commodities may currently be exchanged, via the
mediation of money (so long as markets markets clear, which is not always
the case). It does not follow, however, that a knowledge of these
exchange ratios enable agents to calculate the profitability, let alone
the social usefulness, of producing various commodities. A commodity
can be produced at profit if its price exceeds the sum of the prices of
the inputs required to produce it, using the production method which
yields the least such sum, but the use of current prices in this
calculation is
legitimate only in a static context: either prices are unchanging or
production and sale take zero time. Hayek, of course, stresses
constant change as the rule, so he is hardly in a position to entertain
this sort of assumption. Whether production of commodity x
will in fact prove profitable or not depends on future prices as well as
current prices. And whether production of x currently appears
profitable depends on current expectations of future prices.

If we start from the assumption that prices will almost certainly not
remain unchanged in future, how are agents supposed to form their
expectations? One possibility is that they are able to gather sufficient
relevant information to make a definite forecast of the changes that
are likely to occur. This clearly requires that they know much more
than just current prices. They must know the process whereby prices
are formed, and form forecasts of the evolution of the various factors
(at any rate, the more important of them) that bear upon price
determination. Hayek's informational minimalism is then substantially
breached. A second possibility is that described by Keynes (1936,
esp. chapter 12): agents are so much in the dark on the future that,
although they are sure that some (unspecified) change will occur,
they fall back upon the convention of assuming that tomorrow's prices
will equal today's. This enables them to form a conventional
assessment of the profitability of producing various commodities,
using current price information alone; but the cost of this approach
(from the standpoint of a defender of the efficiency of the market) is
the recognition that those ex ante assessments will be regularly and
perhaps substantially wrong.

It is one of the progressive features of capitalism that the process of
competition forces some degree of convergence upon least-cost
methods of production (even if the cost in question is monetary cost of
production, which reflects social cost in a partial and distorted
manner). Hayek reminds us, and rightly so, that this convergence may
in fact be far from complete. Firms producing the same commodity
(and perhaps even using the same basic technology) may co-exist for
extended periods despite having quite divergent costs of production.
If the law of one price applies to the products in question, the less
efficient producers will make lower profits and/or pay lower wages.
This situation can persist provided the mobility of capital and labour
are less than perfect.

The question arises whether convergence on best practice could be
enforced more effectively in a planned system. We believe this is so.
If all workers are paid at a uniform rate for work done, it will be
impossible for inefficient producers to mask their inefficiency by
paying low wages. Indeed, with the sort of labour-time accounting
system we have advocated elsewhere (Cockshott and Cottrell, 1989,
1993), differentials in productive efficiency will be immediately
apparent. Not only that, but there should be a broader range of
mechanisms for eliminating differentials once they are spotted. A
private firm may realise that a competitor is producing at lower cost,
but short of industrial espionage may have no way of finding out how
this is achieved. Convergence of efficiency, if it is attained at all, may
have to wait until the less efficient producer is driven out of business
and its market share usurped by more efficient rivals. In the context
of a planned system, on the other hand, some of the managers or
technical experts from the more efficient enterprises might, for
instance, be seconded as consultants to the less efficient enterprises.
One can also imagine-in the absence of commercial secrecy-economy-wide electronic bulletin boards on which the people
concerned with operating particular technologies, or producing
particular products, share their tips and tricks for maximising
efficiency. The present popularity of this sort of thing amongst users
of personal computers suggests that it might easily be generalised.

One of Hayek's most fundamental arguments is that the efficient
functioning of an economy involves making use of a great deal of
distributed information, and that the task of centralising
this information is practically impossible.
In what follows we attempt to put this argument to
a quantitative test.
We compare the communications costs implicit in a market
system and a planned system, and examine how the respective costs
grow as a function of the scale of the economy.
Communications cost is a measure of work done
to centralise or disseminate economic information: we
will use the conceptual apparatus of algorithmic information
theory (Chaitin, 1982) to measure this cost.

Our strategy is first to consider the dynamic problem
of how fast, and with what communications overhead, an economy can
converge on equilibrium. We will demonstrate that this can be done
faster and at less communications cost by the planned system.
We consider initially the dynamics of convergence
on a fixed target, since the control system with the faster
impulse response will also be faster at tracking a moving target.

Consider an economy E = [A,c,r,w] with n
producers each producing distinct products under constant returns to
scale using technology matrix A, with a well defined vector of
final consumption expenditure c that is independent of
the prices of the n products, an exogenously given wage rate w and
a compatible rate of profit r. Then there exists a possible Sraffian
equilibrium e = [U,p] where U is the commodity flow
matrix and p a price vector.
We will assume, as is the case in commercial arithmetic,
that all quantities are expressed to some finite precision
rather than being real numbers. How much information is required to
specify this equilibrium point?

Assuming that we have some efficient binary encoding method and
that I(s) is a measure in bits of the information content of the data
structure s using this method, then the equilibrium can be specified
by I(e), or, since the equilibrium is in a sense given in the starting
conditions, it can be specified by I(E)+I(ps) where ps is a
program to solve an arbitrary system of Sraffian equations. In
general we have I(e) £ I(E)+I(ps). In the following we
will assume that I(e) is specified by I(E)+I(ps).

Let I(x|y) be the conditional or relative information (Chaitin, 1982) of
x given y. The conditional information associated with any arbitrary
configuration of the economy, k = [Uk, pk], may then be
expressed relative to the equilibrium state, e, as
I(k|e). If k is in the neighbourhood of e we should expect that
I(k|e) £ I(k). For instance, suppose that we can derive
Uk from A and an intensity vector uk which
specifies the rate at which each industry operates then

I(k|e) £ I( uk)+I( pk )+I( pu )

where pu is a program to compute Uk from some
A and some uk. Since Uk is a matrix and
uk a vector, each of scale n, we can assume that
I( Uk)>I(uk).

As the economy nears equilibrium the conditional
information required to specify it will shrink, since uk starts to
approximate to ue.6
Intuitively we only have to supply the
difference vector between the two, and this will require less and less
information to encode, the smaller the distance between uk
and ue. A similar argument applies to the two price vectors
pk and pe. If we assume that the system
follows a dynamic
law that causes it to converge on equilibrium then we should have the
relation I(kt+1|e)<I(kt|e).

We now construct a model of the amount of information that
has to be transmitted between the producers of a market
economy in order to move it towards equilibrium. We make the
simplifying assumptions that all production process take one timestep to
operate, and that the whole process evolves synchronously. We
assume the process starts just after production has finished, with the
economy in some random non-equilibrium state. We further assume
that each firm starts out with a given selling price for its product.
Each firm i carries out the following procedure.

It writes to all its suppliers asking them their current prices.

It replies to all price requests that it gets, quoting its current
price pi.

It opens and reads all price quotes from its suppliers.

It estimates its current per-unit cost of production.

It calculates the anticipated profitability of production.

If this is above r it increases its target production rate
ui by some fraction. If profitability is below r a proportionate
reduction is made.

It now calculates how much of each input j is required to
sustain that production.

It sends off to each of its suppliers j, an order for amount
Uij of their product.

It opens all orders that it has received and

totals them up.

If the total is greater than the available product it scales
down each order proportionately to ensure that what it can supply is
fairly distributed among its customers.

It dispatches the (partially) filled orders to its customers.

If it has no remaining stocks it increases its selling price
by some increasing function of the level of excess orders, while if it has
stocks left over it reduces its price by some increasing function of the
remaining stock.

It receives all deliveries of inputs and determines at what scale
it can actually proceed with production.

It commences production for the next period.

Experience with computer models of this type of system
indicates that if the readiness of producers to change prices is too
great, the system could be grossly unstable. We will assume that the
price changes are sufficiently small to ensure that only
damped oscillations occur. The condition for movement towards
equilibrium is then that over a sufficiently large ensemble of points
k in phase space, the mean effect of an iteration of the above
procedure is to decrease the mean error for each economic variable
by some factor 0 £ g < 1.
Under such circumstances, while the convergence time
in vector space will clearly follow a
logarithmic law-to converge by a factor of D in
in vector space will take time of order log[1/g](D)-in information space the convergence time will be linear.
Thus if at time t the distance from equilibrium is I(kt|e),
convergence to within a distance e will take a take a time
of order

I(kt|e)-e

dlog(

1
g

)

where d is a constant related to the number of economic
variables that alter by a mean factor of g each step.
The convergence time
in information space, for small e, will thus approximate to a linear
function of I(k|e) which we can write as DI(k|e).

We are now in a position to express the communications costs of
reducing the conditional entropy of the economy to some level e.
Communication takes place at steps 1, 2, 8 and 9c of the procedure.
How many messages does each supplier have to send, and how
much information must they contain?

Letters through the mail contain much redundant pro
forma information: we will assume that this is eliminated and the
messages reduced to their bare essentials. The whole of the pro
forma will be treated as a single symbol in a limited alphabet of
message types. A request for a quote would thus be the pair
[R,H] where R is a symbol indicating that the message is a quotation
request, and H the home address of the requestor. A quote would
be the pair [Q,P] with Q indicating the message is a quote and P
being the price. An order would similarly be represented by
[O,Uij], and with each delivery would go a dispatch note
[N,Uij] indicating the actual amount delivered,
where Uij£Uij.

If we assume that each of n firms has on average m suppliers,
the number of messages of each type per iteration of the procedure
will be nm. Since we have an alphabet of message types
(R, Q, O, N) with cardinality 4, these symbols can be encoded in 2 bits
each. We will further assume that (H, P, Uij, Uij) can
each be encoded in binary numbers of b bits. We thus obtain an
expression for the communications cost of an iteration of
4nm(b+2). Taking into account the number of iterations, the cost of
approaching the equilibrium will be
4nm(b+2) DI(k|e).

Let us now contrast this with what would be required in a planned
economy. Here the procedure involves two distinct procedures, that
followed by the (state-owned) firm and that followed by the planning bureau.
The firms do the following:

In the first time period:

They send to the planners a message listing their
address, their technical input coefficients and their current output
stocks.

They receive instructions from the planners about how
much of each of their output is to be sent to each of their users.

They send the goods with appropriate dispatch notes to
their users.

They receive goods inward, read the dispatch notes and
calculate their new production level.

They commence production.

They then repeatedly perform the same sequence replacing
step 1a with:

They send to the planners a message giving their
current output stocks.

The planning bureau performs the complementary procedure:

In the first period:

They read the details of stocks and technical
coefficients from all of their producers.

They compute the equilibrium point e from technical
coeffients and the final demand.

They compute a turnpike path (Dorfman, Samuelson and
Solow, 1958) from the current output structure to the equilibrium
output structure.

They send out for firms to make deliveries consistent
with moving along that path.

In the second and subsequent periods:

They read messages giving the extent to which output
targets have been met.

They compute a turnpike path from the current output
structure to the equilibrium output structure.

They send out for firms to make deliveries consistent
with moving along that path.

We assume that with computer technology the steps b and c can be
undertaken in a time that is small relative to the production period
(Cockshott 1990, Cockshott and Cottrell 1993).

Comparing the repsective information flows, it is clear that the
number of orders and dispatch notes sent per iteration
is invariant between the two modes of
organisation of production. The only difference is that in the planned
case the orders come from the center whereas in the market they
come from the customers. These messages will again account for a
communications load of 2nm(b+2). The difference is that in the
planned system there is no exchange of price information. Instead, on
the first iteration there is a transmission of information about stocks
and technical coefficients. Since any coefficient takes two numbers
to specify, the communications
load per firm will be: (1+2m)b. For n firms this approximates to
the nm(b+2) that was required to communicate the price data.

The difference comes on subsequent iterations, where, assuming no
technical change, there is no need to update the planners' record of
the technology matrix. On i-1 subsequent iterations, the planning
system has therefore to exchange only about half as much
information as the market system. Furthermore, since the planned
economy moves on a turnpike path to equilibrium, its convergence time
will be less than that of the market economy. The consequent
communications cost is 2nm(b+2)(2 + (i-1)) where
i<DI(k|e).

The consequence is that, contrary to Hayek's claims, the
amount of information that would have to be
transmitted in a planned system is substantially lower than for a
market system. The centralised
gathering of information is less onerous than the commercial
correspondence required by the market. In addition, the convergence
time of the market system is slower. The implication of faster
convergence for adaptation to changing rather than stable conditions
of production and consumption are obvious.

In addition, it should be noted that in our model for the market, we have ignored
any information that has to be sent around the system in order to make
payments. In practice, with the sending of invoices, cheques, receipts,
clearing of cheques etc., the information flow in the market system is
likely to be twice as high as our estimates.
The higher communications overheads of market economies are
reflected in the numbers of office workers they employ,
which in turn leaves its mark on the architecture of cities-witness the skylines of Moscow and New York.

Does Hayek's concentration on the dynamic aspect of prices, price
as a means of dynamically transmitting information, make any
sense?

In one way it does. Consider the price of a cup of coffee.
Notionally this can be written in a couple of digits-80 pence, say-which
would imply that on information theoretic grounds it transmits about
7 bits of information. But look more closely, and this is almost
certainly an overestimate. Not only is the price likely to be rounded
up to the nearest 5 pence, implying an information content of about 5
bits, but yesterday's price was probably the same. If the price
changes only once a year, then for 364 days the only information
that it conveys is that the price has not changed. The information
content of this, -log2 [364/365], is about 0.0039 of a
bit. Then when the price does change its information content is
-log2 [1/365] + b where b is the number of bits to
encode the price increase. For a reasonable value of the increase,
say 10 pence, the whole amounts to some 12 bits. So on the day the
price changes, it conveys some 3000 times as much information as
it did every other day of the year.

So it is almost certainly true that most of the information in a price
series is encoded in the price changes. From the standpoint of
someone observing and reacting to prices, the changes are all
important. But this is a viewpoint internal to the dynamics of the
market system. One has to ask if the information thus conveyed has
a more general import. The price changes
experienced by a firm in a market economy can arise from
many different causes, but we have to consider which of these
represent information that is independent of the social form of
production.

We can divide the changes into those that are direct results of
events external to the price system, and those which are internal to
the system. The discovery of new oil reserves or an increase in the birth rate
would directly impinge upon the price of oil or of baby clothes. These
represent changes in the needs or production capabilities of society,
and any system of economic regulation should have means
of responding to them. On the other side, we must count a fall in
the price of acrylic feedstocks and a fall in the price of acrylic
sweaters, among the second- and third-order internally generated
changes consequent upon a fall in oil prices. In the same category
would go the rise in house prices that follows an expansion of
credit, any fluctuation in share prices, or the general fall in prices
that marks the onset of a recession. These are all changes
generated by the internal dynamics of a market system, and as such
irrelevant to the consideration of non-market economies.

Hayek is of course right that the planning problem is greatly simplified if there
are no changes, but it does not follow from this that all the changes
of a market economy are potential problems for a planned one.
We have demonstrated elsewhere that the problem of computing
the appropriate intensities of operation of all production processes,
given a fully disagregated input-output matrix and a target final output
vector, is well within the capacity of computer technology. The
compute time required is sufficiently short for a planning authority,
should it so wish, to be able to perform the operation on a daily
basis. In performing this calculation the planners arrive at the
various scales of production that the market economy would
operate at were it able to attain general equilibrium. Faced with an
exogenous change, the planners can compute the new equilibrium
position and issue directives to production units to move directly to
it. This direct move will involve the physical movement of goods,
laying of foundations, fitting out of buildings etc, and will therefore
take some considerable time.

We now have two times, the time of calculation and the time
of physical adjustment. If we assume that the calculation is
performed with an iterative algorithm, we find that in practice it will
converge acceptably within a dozen iterations. Since each of these
iterations would take a few minutes on a supercomputer the overall
time would probably be under an hour. In a market economy, even
making the most favourable assumptions about its ability to adjust
stably to equilibrium, the individual iterations will take a time
proportional to the physical adjustment time. The overall relaxation
period would be around a dozen times as long as that in the planned
system.

But of course these assumptions are unrealistically favourable to
the market system. Long before equilibrium was reached, new
external shocks would have occurred. Even the assumption that the system
seeks equilibrium is questionable. There is every reason to believe
that far from having stable dynamics, it is liable to oscillatory or
chaotic behaviours.

Hayek is to be commended on his ability to make the best of a bad
case, to make virtues out of necessities. The unavoidable
instabilities of the market are disguised as blessings. The very
crudity of prices as an information mechanism are seen as
providentially protecting people from information overload.

Hayek contrasts the `spontaneously evolved' price system
with the artificiality of conscious attempts to control
the economic process, a contrast that he feels is to
the disadvantage of the latter.
At best, this is no more than the maxim that one is better
to `hold tightly onto nurse for fear of meeting something
worse'. At worst it degenerates into a Panglossian complacency
about the existing order of things. Voltaire's rejoinder on
earthquakes-these too are spontaneous-is apposite.
But while we can hope to do no more than
forecast earthquakes, it fallacious to think that we are forced
endure their economic equivalent with the same stoicism.

By writing of spontaneous evolution, Hayek surreptitiously
slips in connotations from biology, with its
associations of fitness of form to function.
But the analogy of a market economy with a naturally evolved
order is superficial,
with regard both to its operation and genesis.
If we consider the operation of a market
economy as the procedural search for an optimum,
it obvious that while there is a
great deal of parallelism going on-lots of people making decisions at
the same time-it remains the case that the whole search is
single-threaded. Taken as a whole, the state space of the economy
is a Cartesian product of the state spaces of its components, and
within this total state space the economy is located at a unique
point at every moment in time. As such, it can only visit a small
proportion of the possible set of solutions, and for it to progress
towards anything other than a local optimum presupposes a
particular and very simple topology to the space.

In this sense, the movement of a market economy differs
from the process of biological evolution. A species evolves towards
increasing adaptation to its environment by a highly parallel process.
The state space in this case consists of the genetic code. But a
species is not in one position in this space at any one time: it is at as
many positions as there are individual members of the species, each
with a unique combination of genes. A species represents a
neighbourhood in gene space. It applies a parallel search procedure:
millions of alternative designs are produced and compared each
generation. Although a market economy can to some extent
emulate this in the area of product development within individual
competitive markets, the economy as a whole acts as a single
processor.

It equally invalid to treat the genesis of the capitalist world
system as an evolutionary outcome. It is an historical outcome,
but history and evolution are not the same thing. Evolutionary
adaptation is impossible without variation, competition and
selection. To apply evolutionary concepts one would have to
hypothesise a substantial population of simultaneously existing
international economic systems. In fact there is only one. For a while
there were two, of which only one has survived. That
is not a statistically valid sample. To say that one
economic order was evolutionarily better adapted than another,
one would need a large enough ensemble for stochastic effects
to cancel out-an ensemble including instances where the market system was
restricted to one poor and backward economy surrounded by
an industrialised socialist world.

The logic of the analogy with evolution, contra Hayek, is to
let a hundred flowers bloom.

References

-.05in

Althusser, L. (1971).

`Ideology and ideological state
apparatuses'. In Lenin and Philosophy and Other Essays .
London: NLB.

`Notes on the Sraffa-Hayek
Exchange', Review of Political Economy , vol 4.

Lawson, T. (1992).

`Realism and Hayek: a case of continuous
transformation', mimeo, University of Cambridge.

Mises, L. (1949).

Human Action: A Treatise on Economics .
New Haven: Yale University Press.

Nove, A. (1977).

The Soviet Economic System .
London: George Allen and Unwin.

Nove, A. (1983).

The Economics of Feasible Socialism .
London: George Allen and Unwin.

Shannon, C. E., and Weaver, W. (1949).

The Mathematical Theory
of Communication . Urbana, Ill.: University of Illinois.

Footnotes:

1 Our ideas were first presented in Cockshott and Cottrell (1989), and are set out most fully in Cockshott and Cottrell (1993). Cottrell and Cockshott (1993a) re-examines the historic socialist calculation debate, with emphasis on the arguments of Mises and Lange. In Cottrell and Cockshott (1993b) we stress the differences between our proposals and the system that existed in the Soviet Union. Technical details of the algorithm we propose for short- to medium-term planning are spelled out in Cockshott (1990).

2 Take the homely example of Christmas shopping. Many of us find it impossible to draw up a complete plan for such shopping in advance. We have to go to the shops, look at the goods and their prices, and see what strikes our fancy. Our `demand functions' are revealed to ourselves in the act of choosing.

3 Admittedly, such an image does not of itselfprovide any information on how, for instance, a particularlyfavourable set of input-output relations can be achieved , only thatit is possible . We offer some further thoughts on thetransmission of such `know how' in Section 6 below.

4 Although Nove's case is surely exaggerated in one respect: if the central plan calls for enterprise A to supply intermediate good x to enterprise B, where it will be used in the production of some further good y, and if the planners apprise A and B of this fact, surely there is scope for horizontal discussion between the two enterprises over the precise design specification of x, even in the absence of market relations between A and B.

5 The specific reference here is to p. 43, and more particularly tonote 37 on pp. 212-213, of The Counter-Revolution of Science . In the note, Hayek appeals to the judgment of Pareto and Cournot, thatthe solution of a system of equations representing the conditions ofgeneral equilibrium would be practically infeasible. This is perhaps worth emphasising in view of the tendency of Hayek's modern supporters to play down the computational issue.

6 Note that this information measure of the distance from equilibrium, based on a sum of logarithms, differs from a simple Euclidean measure, based on a sum of squares. The information measure is more sensitive to a multiplicity of small errors than to one large error. Because of the equivalence between information and entropy it also measures the conditional entropy of the system.